TY  - JOUR
PB  - SciPost Foundation
DO  - 10.21468/SciPostPhysProc.14.045
TI  - Construction of matryoshka nested indecomposable N-replications of  Kac-modules of quasi-reductive Lie superalgebras, including the sl(m/n) and osp(2/2n) series
PY  - 2023/11/24
UR  - https://scipost.org/SciPostPhysProc.14.045
JF  - SciPost Physics Proceedings
JA  - SciPost Phys. Proc.
VL  - 
IS  - 14
SP  - 045
A1  - Thierry-Mieg, Jean
AU  - Jarvis, Peter D.
AU  - Germoni, Jerome
AU  - Gorelik, Maria
AB  - We construct a new class of finite dimensional indecomposable representations of simple superalgebras which may explain, in a natural way, the existence of the heavier elementary particles. In type I Lie superalgebras sl(m/n) and osp(2/2n), one of the Dynkin weights labeling the finite dimensional irreducible representations is continuous. Taking the derivative, we show how to construct indecomposable representations recursively embedding N copies of the original irreducible representation, coupled by generalized Cabibbo angles, as observed among the three generations of leptons and quarks of the standard model. The construction is then generalized in the appendix to quasi-reductive Lie superalgebras.
ER  -

@Article{10.21468/SciPostPhysProc.14.045,
	title={{Construction of matryoshka nested indecomposable N-replications of  Kac-modules of quasi-reductive Lie superalgebras, including the sl(m/n) and osp(2/2n) series}},
	author={Jean Thierry-Mieg and Peter D. Jarvis and Jerome Germoni and Maria Gorelik},
	journal={SciPost Phys. Proc.},
	pages={045},
	year={2023},
	publisher={SciPost},
	doi={10.21468/SciPostPhysProc.14.045},
	url={https://scipost.org/10.21468/SciPostPhysProc.14.045},
}